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Results tagged with at.algebraic-topology
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user 960
Homotopy theory, homological algebra, algebraic treatments of manifolds.
6
votes
How does Poincare duality interact with the Serre spectral sequence?
After thinking about this for a little while, it seems like there is a satisfactory way of carrying this out in group cohomology using the Hochschild-Serre spectral sequence of a group extension
$$1 …
- 2,830
22
votes
1
answer
1k
views
How does Poincare duality interact with the Serre spectral sequence?
Suppose $F^m \to E^{m + n} \to B^n$ is a fiber bundle of closed oriented manifolds. I'm interested in understanding how the Serre spectral sequences for homology and cohomology of $E$ interact with ea …
- 2,830
19
votes
1
answer
959
views
Does there exist a surface bundle over a surface of genus at least 2 that fibers in three di...
Let
$$
\Sigma_g \to E \to \Sigma_h
$$
be a surface bundle over a surface. Unless otherwise stated, I'll assume $g, h \ge 2$. The theory of Thurston norm shows that surface bundles over $S^1$ often fi …
- 2,830
14
votes
Accepted
Does there exist a surface bundle over a surface of genus at least 2 that fibers in three di...
Yes. I recently found methods of constructing surface bundles over surfaces with at least $n$ fiberings for any $n$. The idea is to perform a fiberwise connect-sum of trivial bundles in such a way tha …
- 2,830
11
votes
1
answer
777
views
What is an interpretation of the relation in the cohomology of the pure braid groups?
In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{i,j}\ (1 \le i < j \ …
- 2,830